How can I remove the noise from an EEG signal?
This might be more of a signal-processing question, rather than a artificial intelligence question, but I will try my best to be of help.

Do you know what the noise you are trying to remove is? How it behaves/where it stems from?
Or, do you know how your output signal should look, post processing?

If you know these things and you are familiar with MATLAB or any other matrix multiplication software, they come with great prebuilt toolboxes for traditional approaches to remove noise from signals.

If you are not exactly sure what patterns you are looking for, I suggest perhaps looking into Autoencoders to discover the hidden patterns. Though it is important to note that the origin of the noise may greatly effect its abilities.
If you plan on using such a technique it is important that you have a sufficiently large dataset of the signals available.

Without the clarifications to these questions, along with @nbro's questions, it is hard to be more specific.